# How to extrapolate the curve that connects airfoil coordinates for aerodynamic shape carved into foam by hand without CAD?

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#### MotoFairing

##### Active Member
Hello I want to carve an aerodynamic shape based on horizontal and vertical airfoil coordinates and a single cross section to ensure fit then extrapolating to every airfoil coordinate along the body.

How can I extrapolate this curve?

I have seen the Arnold Company videos where he uses templates which are based on scale models. I don't have his skill so will need a method to find the curve.

Here is the surf board method, the height and width are cut first with wooden hot wire templates, then the corners are progressively cut off to reveal the curve.
Pictures of the project are here: Project Sanderson. AV-ACG

Here is the stacked slice method although the slices in the example were derived from CAD which I don't understand. If the curve can be discovered the slices might be able to be done without CAD although I imagine it would be time consuming with 60, 4cm slices for example.
Pictures from here: The Recumbent Bicycle and Human Powered Vehicle Information Center

This seems a bit magical as I don't yet understand how the find that curve for the surf board method or for the stacked slice method.

#### Dana

##### Super Moderator
Staff member
I really have no idea what you're asking for.

Traditionally (pre-CAD) airfoils are drawn by first drawing a grid and plotting the upper and lower surface points from a table of airfoil X-Y data. Then drafting curves (french curve, ship's curves, or flexible splines) are used to draw smooth curves through the points. Also see Lofting - Wikipedia

#### TFF

##### Well-Known Member
Pretty much what Dana says. You can have some templates at key points for checking progress. It’s all connect the dots. At some point you have to put the artist hat on and make it smooth. The amount of dots you want to use is up to you.

Airfoil for a wing, you make a 5 ft sanding block for sanding across the span and start sanding. It’s how most Rutan designed planes had to be built until not too long ago. Foam sands very easy, so it’s not heavy loads. If you get it wrong, you slice another chunk of foam off, glue it where you went too far, and sand down.

Big cuts can be done with hacksaw blades, electric kitchen knives, and you get progressively finer with planes, and knives, and sandpaper.

There is also hot wire cutting if it’s the right kind of foam.

#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
I also am not sure exactly what you are trying to do. If you are trying to make a shape similar to the one in your post then you either do it by hand using your eye or create the templates if you need that kind of precision.
The old school way of creating the templates by hand drawing is tedious and rather complex. IMHO it would probably be easier to learn one of the free CAD programs than learn the old school method.

#### Hephaestus

##### Well-Known Member
What was the program - devfuse?

There it is - that one's been the 'easy learning' cad and NC system from the RC world... It's been super simplified; but if you're wanting "Bigger" its fairly easy to fudge the numbers to make inches feet and scale that small part to bigger.

#### Jay Kempf

##### Curmudgeon in Training (CIT)
There is no one method. "Fair" curves are just that. You can do it by hand or by computer. By hand you need to do what is called "lofting" in each of the 3 Axis. You need cross sections that fit what you want to fit in. So each bulkhead or fuselage station is a shape at the hips, shoulders, feet, etc... The top fattest cross section depending on the location of the cross section is either based on a curved plane or a flat plane depending on your design. The side sections are interpolated from the other two direction. Look for drafting books on "lofting" techniques. The boat building world is full of them.

I would loft onto walls and floor and use strings, squares, plumb bobs, etc... to find points in space. Then you transfer those curves to the chunk of material you are working with one layer at a time.

#### TFF

##### Well-Known Member
I prefer the old way, easier for me. My CAD learning has been like trying to learn Latin in 8th grade. To me building is an artistic endeavor. I like the hand work. When it resembles production, I tune out. I’m not the old guy either.

#### WonderousMountain

##### Well-Known Member
It's a polynomial fit equation that runs through our data points, only a handfull of people on the planet have enough training to comprehend the math, design principles and experiance to make it work. There aren't any virtual rules of thumb to give.

#### wizzardworks

##### Well-Known Member
Motofaring, I think it would be helpful to show us a "napkin sketch". Just a freehand drawing of the shape you are trying to make. Also
include where the single airfoil coordinates shape is on the body you are trying to carve. Based on intuition alone I think you are using a symetrical airfoil shape for low drag, probably at the widest cross section then making it progressively smaller above and below that
widest point following a shape in a plane drawn 90 degrees to the airfoil shape. Based on this I would further GUESS that the above and
below shapes will be different dictated by what internal things the shape is covering. I built a 3D hotwire cutter 25 years ago which is
still sitting outside my machine shop. Basically 2" thick slabs of foam are curved to a shape longitudinally then hot wired on the 90
degree axis by templates using 2 hot wires for the inside and outside surfaces. The 2 hotwires equalize heat stress warping and make a consistant thickness "shell" for an aircraft fuselage. After cooling the piece is released and it springs into a compound curve shape. For
your Thing you might consider a pantograph to do the interpolation. Just set it for the width of the airfoil cross section and let the pantograph scale the height above the section. Do the bottom separately. Your check template is what you run the pantograph on. Please excuse
spelling errors because my dog does the typing and he never finished obedience school.

#### proppastie

##### Well-Known Member
Log Member
I don't yet understand how the find that curve
graph paper .....make dots of the coordinates of the airfoil .....connect the dots.....paste to some foam ....cut out along the lines, ......take some sand paper and smooth it......unless you are saying you do not understand how to plot the airfoil......in which case take a picture and have Kinkos blow it up the the size you want and then cut it out and paste to some foam

#### ScaleBirdsScott

##### Well-Known Member
A bunch of points on a plane and a long bendy strip of material give a good curve. The old heads might mention things like lofting whales or drafting ducks or similar. Lead weights with a pointy bit to help anchor the bendy strip in place.

Once it gets into 3D curves you need more planes and bendy sticks, maybe bendy rods. Setup sufficient references to constrain the form. And then let the eye and hand coordinate a curve to suit.

#### wizzardworks

##### Well-Known Member
Motofaring, There is a free program called xflr5 that is mostly used for analyzing wing lift drag and moments. If you go to UIUC
airfoil database you can download the .dat file of X and Y coordinates. They are actually percents but if you plot them you get a
100 inch long airfoil. Save the .dat file on UIUC and open it in xflr5. Use print in windows to save the viewport. In the print preview
you can specify a scale. If you leave it as 1" on the screen = 1" on the print you get a 100 inch long airfoil. At the top you specify
the paper size like 24" or 30" height and 105 " long, and landscape view. Anyway you do it is OK if you get the scale up to something
near what you need. Take the saved file to a print shop that offers "large Format Printing" with a roll feed on the paper. They will
crop the image down to what you need from the xflr5 saved image and then scale it to anything up to the width of the paper roll.
I have a 24" HP roll feed in my machine shop that I use a LOT, and a 72" wide dye sup graphics printer I rarely use. There is a 48"
pen plotter as well so we can do inhouse but mostly send the file electronically to a shop called "Microcad" these days since we
moved to the Philippines and all the printers are in the US. Cost is about \$10 for a 9 foot long print on a 32" wide roll feed HP.
Once you have the base shape they can scale it "differentially" which means different X and Y scale factors. Microcad is also a
CAD school for autocad. If you furnish the X and Y scale list they will nest a bunch of them on a single print and save a lot of the
printing cost.
You might take a look at design of Whitman winglets which on my plane are angled in 2.3 degrees and flow analysis shows
them making a forward thrust vector larger than the drag. If you are using the airfoil shape vertically and tilt the chord line up on
the rear end some interesting things might be possible. Well got to go the dog is drinking out of the toilet....again.

#### wizzardworks

##### Well-Known Member
Motofaring, Just thinking, I did a thread called "how I am building a fuselage mould" also posted by wizzardworks which has plenty
of pictures with too long explanations but you might get an idea or two from it.

#### MotoFairing

##### Active Member
If I have the width and the height, I need to connect those two points with a curve.

I have a hot wire cutter, random orbital sander, angle grinder, saws, sand paper, soft sanding blocks from the surf board shop, a sharpie and a rule. I don't have great sculpting skill as seen in my recent luggage box project so need a methodical approach to sculpting a symmetrical shape.

Motofaring, I think it would be helpful to show us a "napkin sketch". Just a freehand drawing of the shape you are trying to make. Also
include where the single airfoil coordinates shape is on the body you are trying to carve. Based on intuition alone I think you are using a symetrical airfoil shape for low drag, probably at the widest cross section then making it progressively smaller above and below that
widest point following a shape in a plane drawn 90 degrees to the airfoil shape. Based on this I would further GUESS that the above and
below shapes will be different dictated by what internal things the shape is covering. I built a 3D hotwire cutter 25 years ago which is
still sitting outside my machine shop. Basically 2" thick slabs of foam are curved to a shape longitudinally then hot wired on the 90
degree axis by templates using 2 hot wires for the inside and outside surfaces. The 2 hotwires equalize heat stress warping and make a consistant thickness "shell" for an aircraft fuselage. After cooling the piece is released and it springs into a compound curve shape. For
your Thing you might consider a pantograph to do the interpolation. Just set it for the width of the airfoil cross section and let the pantograph scale the height above the section. Do the bottom separately. Your check template is what you run the pantograph on. Please excuse
spelling errors because my dog does the typing and he never finished obedience school.
I am currently making the bicycle frame so cannot settle on a specific shape until I have have that sorted. Then I can measure the required clearances for feet, knees, hips, shoulders and head.

I can select a laminar airfoil for the vertical and horizontal planes, that fits. Some vehicles use airfoils that work better in ground effect.

Others are symmetrical which also means only one half needs to be molded.

I will probably have a head bubble if I decide molding a large canopy is too hard.

#### Dana

##### Super Moderator
Staff member
Take your chosen shape, plot the points and draw the curve onto pieces of cardboard. Cut along the curve and use the female side as you shape the foam until it fits into the template. For what you're doing the precise shape probably isn't that critical, but by using the templates you can get it consistent and symmetrical.

#### wizzardworks

##### Well-Known Member
It's a polynomial fit equation that runs through our data points, only a handfull of people on the planet have enough training to comprehend the math, design principles and experiance to make it work. There aren't any virtual rules of thumb to give.
Math consists of addition, subtraction, multiplication, and division. Integral Claculus, Differential equations, analytic geometry, and
algebra are all just ways to organize which operation you do and what order to do them. To use a formula, plug in the numbers and
work from the inside of brackets outward. You don't have to fit Euler equations to grind out an answer. The relevent equations are in
"Theory of Wing Sections" which is what Harry Ribblet used to fill in the nose of airfoil shapes that during WW2 were done with a
leading edge radius to expidite making wind tunnel test sections. The reason that the published data while relevent for comparison
but not actual value was that Langley used 7" long sections with about a 6" chord in their wind tunnel. And that is where the published
data originated. When we use the coordinates of a .dat file in CAD it draws what the curve should be, not a leading edge radius.

#### wizzardworks

##### Well-Known Member
If I have the width and the height, I need to connect those two points with a curve.
View attachment 118488
I have a hot wire cutter, random orbital sander, angle grinder, saws, sand paper, soft sanding blocks from the surf board shop, a sharpie and a rule. I don't have great sculpting skill as seen in my recent luggage box project so need a methodical approach to sculpting a symmetrical shape.

I am currently making the bicycle frame so cannot settle on a specific shape until I have have that sorted. Then I can measure the required clearances for feet, knees, hips, shoulders and head.

I can select a laminar airfoil for the vertical and horizontal planes, that fits. Some vehicles use airfoils that work better in ground effect.
View attachment 118494
Others are symmetrical which also means only one half needs to be molded.
View attachment 118495

I will probably have a head bubble if I decide molding a large canopy is too hard.
OK!!!! In your cross sections note that the curve is tangent to the cut lines. So... at the tangent points draw a line perpendicular
to the cut lines for two adjacent cut lines. from where they intersect scribe a circle that goes thru the two cut line points. You
may be seeing two different distances. Take one using the others tangent point as a center and strike an arc. Do the reverse
for the other tangent. Half way between the old and new crossing points is the center point for that section of arc. What you
are showing as blue cut lines may need what would be the equivalent mirror image to use as the next tangent point.
Not telling you your business, but if you look on wikipedia on how to draw an elipse you can do a top elippse and a bottom
elippse which will be lower drag. The join line for the elippse can follow where you want the widest part of the section to be
usually passing through shoulder height and lower forward and aft of that. Make cross sections 2" apart on the nose and
multiples of 2 inches for the rest of the thing. You will need a reference height above the table for each cross section. Drill
a pair of holes through all the templates stacked up at the reference height for like 1/2" PVC pipe Cut the templates out
of 3/16" plywood. Starting in the center mount a template. Drop in rough cut blanks of 2" blue foam to the next station. Mount
that template, drop in foam add a template....repeat. You can glue the foam to foam well inside the contour but not near
where you will be sanding. Once stacked up sharpen a piece of copper pipe and work it through all the templates and foam
so that you can compress the stack lengthwise with two 1/2" threaded rods. Now chop, saw, hotwird sand whatever the foam
outside the templates till you are within 3/4" of the template edges. Then using a very long flexible sanding block sand
diagonally till within 1/8" of the templates. You can use a belt sander belt cut for a 3 foot long piece of sandpaper. Start
with 24 or 36 grit. Once rough contoured draw lengthwise lines down the thing for realigning the parts. Pull out the threaded
rods and templates and replace the templates with 1/4" foam sheet. Back with the threaded rods lined up by the witness lines.
Switch to 120 grit sandpaper and sand till the contour is as faired as your skill level permits. You are making a plug so if you
want to wipe on some drywall compound or plaster of paris you can do that. The smoother you make the plug the less micro
you will have leveling the actual parts. Make generous clearance on the rear half of the front wheel to bring in cooling air and
leave an outlet in the tail end for cooling. Split the faring as a top and bottom to get it off the plug but rejoin any areas you can
past what it takes to get in and out for maximum laminer flow. Don't know about any canopy. Cooler breathable air seems
more important possibly fit the tailcone to your helmut shape ?

#### MotoFairing

##### Active Member
Busy day today, I showed the pictures to a local foam manufacturer. He said with his 2D machine he can cut the top and side view into a block of "m" grade polystyrene. "M" grade is used for surf boards is a bit smaller and better for sanding he says.

He needs:
1) DXF file with both profiles and the dimensions (height, width, length) so he can scale it correctly.
2) PDF of both profiles in case he needs to draw the line then mirror.
He mentioned "vector" because his machine follows lines and lines will give the smooth shape.

I will try to get this quote so I can see if this is an affordable option. With this accurate starting point I could draw a bunch of dots and bendy strip them into a line with my sharpie. Sanding off the corners within the lines with a 3 foot long sanding block is within my ability.

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#### wizzardworks

##### Well-Known Member
Motofaring, Most software that does DFX (Drawing Exchange Format) is CAD software. DFX was a later edition of the Autocad file
extensions because they made their .DWG propriatary. Most software saves to DFX. On the other hand PDF is more of a text
based file like Microsoft Office, or the free open source "Open Office" by Apachie. I think a JPG file extension also available as a
"print selected" operation in CAD is what you need. That would duplicate the curves and be scalable. You will need a napkin sketch
of your bicycle frame with wheels frame tubing pedal clearance lines, height and width of things that need to fit within your shell
and their location from some point out in front of the thing. Plenty of forum members that would loft your shape, to print the profiles
and cross sections templates. What I do is put a measuring standard of exactly one meter long lines both lengthwise and crosswise
on prints so the print shop can verify their settings. You are working with one inch on the model = one inch on paper so it would
seem foolproof, but it don't hurt ta check. You realize of course that once you can print top and side views you can hotwire the block
of foam up to about 32" thicknesses and more with nichrome wire and a little patience. If your foam can't be hotwired a big homebrew
bow saw using a piece of bandsaw blade could be run along the templates. If you care to say where you are located someone may
know of a 3D foam cutter near you. Well time to start dinner....AGAIN. the dog just pulled the skillet off the stove. So how long do
dogs live without human intervention?